When India's government-run television recently inserted 15 minutes of Hindi-language news to its nightly broadcast to this Tamil-speaking southern Indian region, the howls of protest were so great that the program had to be scrapped hastily.

Similarly, Prime Minister Indira Gandhi yielded to Tamil pressure and reversed a decision to rename All India Radio "Akashvani," which is a Sanskrit word meaning "sound in the air" but which sounded Hindi enough to outrage Tamils.

Linguistic pride has spawned three regional parties that dominate politics in Tamil Nadu state and another that threatens to unseat Gandhi's Congress-I Party in neighboring Andhra Pradesh in state elections next month.

In the northern state of Punjab, militant Sikhs demanding sweeping autonomy and an enlarged Punjabi-speaking state are continuing a four-month-old campaign of civil disobedience that has left 44 persons dead in riots and more than 30,000 jailed.

Fears of ethnic and linguistic extinction because of the influx of Bengalis from Bangladesh are fueling almost daily protests in the northeastern state of Assam. In the tiny and remote Indian states to the east, government troops continue their sporadic battles with armed separatist insurgents.

Even in Goa, the former Portuguese resort colony that India forcibly annexed in 1961, a regional movement was begun this week, calling itself "real Goans." The group is demanding that statehood be granted for Goa -- without the mainland districts of Daman and Diu -- and that Konkani be made the official language.

The centrifugal forces of regionalism that have been a part of India since it won independence 35 years ago are showing signs of spreading and are tugging increasingly at the fabric of society and the federal government.

While the Indian union remains strong and Gandhi continues to display considerable dexterity in managing regional crises as they occur, the resistance to national integration by some states poses a political threat to her Congress-I Party, which together with its predecessor, the Congress Party, has dominated politics for most of the time since India gained independence in 1947.

State assembly elections on Jan. 5 in Andhra Pradesh and Karnatakan, both Congress-I stronghold states in southern India, are being watched closely as indicators of Gandhi's potential in the national elections within the next two years.

In both states, as elsewhere in India, the ruling Congress-I is torn by rivalries between longtime party loyalists and opposition defectors who recently came to support Gandhi and, to the annoyance of the loyalists, are being rewarded.

The balloting also is expected to influence Gandhi's decision on calling a date for general elections, which must be held no later than 1985.

Paradoxically, the regional strains on the union and the Congress-I Party are increasing at a time when Gandhi has accumulated unprecedented power by breaking up entrenched state party organizations and putting her loyalists in power at the local level.

Gandhi lately has stepped up her warnings about regionalism, rhetorically lumping together language and ethnic opposition groups into a single, shadowy subversive element that threatens the unity and integrity of India.

In a tour of Andhra Pradesh this week, she vaguely linked the regional parties with external divisive forces, and in an appeal to patriotism, she asked voters to be vigilant against forces "seeking to harm the cause of national integration."

Anti-Hindi sentiment is not the only symptom of regionalism in India, but in the southern portion of this vast subcontinent it is the most important. Since the boundaries of the country's 22 states are drawn roughly along the lines of the 15 official languages, the potential for the symptom's spreading is significant.

India's 1949 constitution proclaimed Hindi as the official national language, but the framers, in a display of realism, decreed that English would continue to be used as a link language for official purposes for 15 years while the government promoted the spread of Hindi.

In 1965, with English still firmly entrenched as the national link language and regional languages as strong as ever, the government decreed that Hindi, which is spoken as the mother tongue by about 38 percent of India's 800 million people, would be imposed in contacts between the central and state governments.

Protest erupted in Tamil Nadu, during which rioters destroyed Hindi signs and attacked government offices and eight students burned themselves to death. The government reverted to its policy of gradual promulgation of Hindi, retaining both Hindi and English as the official languages of the central government and permitting non-Hindi states to conduct business with the central government in their own languages.

"The battle against Hindi has not yet ended," Muthuvel Karunanidhin, president of the Dravidian Progressive Party here and former Tamil Nadu chief minister, or governor, said in an interview. "If the mother tongue of certain states becomes the national language, it will naturally result in the supremacy of those states over others in the non-Hindi belt. We want all national languages to be given equal status with the center. Until we reach this stage, English must remain the link language."

The Dravidian parties grew out of a movement that in the 1920s overthrew the minority Brahmin caste domination here and later, at the time of independence, sought to secede from the union as a Tamil-speaking state. They dominate political life among the state's 40 million Tamils.

The current chief minister, Marudar G. Ramachandran, of the splinter All-India Dravidian Progressive Party, a former matinee idol of Tamil films, has capitalized on anti-Hindi sentiment to build a strong political power base, just as another film star, N. T. Ram Rao, has seized upon pride in the Telugu language to mount his strong challenge in neighboring Andhra Pradesh.

A week before national television abandoned its Hindi newscast here, Ramachandran called on Tamils to switch off their television sets when "we see or hear programs in a language that we do not understand or like."

Karunanidhi maintained, however, that it is not simply language chauvinism that motivates defenders of Tamil, but a fear of domination by the Hindi-leaning central government and a loss of autonomy.

The scrapping of Hindi television news and the dropping of All India Radio's new name, Karunandhi said, "has only offered false bait to win the good will of the Tamils. These were only the thin end of the wedge . . . not to speak of the subtle but sure imposition of Hindi already under way."

Some longtime observers of Tamil Nadu politics insist that regionalism spawned out of linguistic pride is an artificial movement generated by cynical politicians who seek to gain or retain power by exploiting an emotional issue.

Saeed Naqvi, a political commentator here for the Indian Express, called the phenomena of Ramachandran and Rama Rao "cinematic charisma with a potent mix of linguistic chauvinism." But he added in an interview, "This formula won't work indefinitely. Film stars and language chauvinists may be a fad, but they can't continue to attract politically motivated voters."

The language issue, Naqvi complained, merely has served to deflect attention from Tamil Nadu's problems, including an ailing economy and a critical energy problem that has been exacerbated by severe drought and has resulted in power cutbacks of hydroelectric plants in the state.

But Naqvi said that intense regionalism could cut sharply into Gandhi's Congress-I Party base in southern India and that the coming state elections are important in that regard.

A Western diplomat here who has monitored southern Indian politics for years, agreed. "If regionalism takes off in Karnataka," he said, "and the Telegu people take off in Andhra Pradesh, we will have to take a serious look at what is happening."

But the diplomat added that at the moment Gandhi retains "impressive clout" in the region.

At the other end of the spectrum are Hindi-speaking politicians, mostly from the northern regions, who bitterly complain that the constitutional imperative for one national language is being ignored by a central government that has been intimidated by extremists.

Indeed, English continues to be the language of power, politics, commerce and higher education, even though it is spoken by less than 3 percent of the Indian population. There are more English-language schools than ever before; English-language newspapers dominate Indian journalism, and nearly 80 percent of advertising in India is in English. Even Gandhi and other top officials conduct their press conferences in English routinely.

Ranjath Sonkar Shastri, parliamentary whip for the opposition People's Party, blamed the Gandhi government for the failure of Hindi to take hold as a national language.

Even after 35 years, Shastri said in an interview, "independence is not really successful because nobody talks of the nation. Each person talks only of self, caste, region and language. These divisive tendencies are all post-independence creations, and since the Congress Party has been in power for all but 2 1/2 years it is to blame."

Shastri said if the government wanted to, it could make Hindi the national language in six months by enforcing its use in Parliament, government agencies, state banks, post offices and courts of law. At the current rate, Shastri complained, "Hindi will not achieve national stature even after another 35 years."

But the government, wary of past regional eruptions over the imposition, continues to follow a cautious policy of gradualism, hoping to succeed with good will.

"The idea is to strengthen the country, not to divide it. We are committed to a progressive use of Hindi and we are making headway," said D.P. Bhal, deputy secretary of the Department of Official Language.

He said salary raises and cash bonuses are being offered to government employes who accept Hindi language training and that an increasing number of official documents are being published in Hindi as well as English.

Language passions in India, and subsequently the phenomenon of regionalism, tend to rise and fall. With few exceptions, regional movements have not taken a separatist turn, or even a serious anti-Indian turn, presumably because the states appreciate their financial dependency on the central government.

Gandhi, apparently mindful of the potential for fragmentation of the union, clearly has decided to let Hindi spread on its own accord, with a minimum of attention generated by national leaders.

However, the imponderable remains whether regional political forces in this vast, diverse mosaic of cultures will allow the debate over language to simmer quietly or whether they will force it to confrontation with Gandhi's ruling party and erode the prime minister's formidible base of power.